Viscous Flow of a Suspension of Deformable Liquid Drops in a Cylindrical Tube

摘要

Viscous flow in a circular cylindrical tube containing an infinite line of deformable liquid drops equally spaced along the tube axis is considered. The fluid within the drops as well as the suspending fluid is taken to be Newtonian and incompressible. A surface tension is assumed to act at the interface. Two types of solutions are developed depending on the magnitude of the distortion of the drop shape from spherical. A perturbation solution is employed for nearly spherical drops. In this case the flow of the suspending fluid and liquid drops under an imposed pressure gradient is a linear combination of the solutions obtained for (1) the axial translation of the drops, and (2) the flow of the suspending fluid past the drops. For large deformations the problem is no longer linear in these two flows. An approximate numerical technique is employed for this case which yields the drop shape as well as the other parameters of the flow. The results show that both drag and pressure loss per drop increases with both increasing drop spacing and radius. The internal motion of the drops reduces the drag and pressure gradients as compared with rigid spheres of equal volume. Further, due to the deformation, the overall resistance decreases with increasing flow rate. This constitutes a mechanism of non-Newtonian behavior of the suspension as a whole. (Author)